Question: The sum of two numbers is $69$, and their difference is $7$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 69}$ ${x-y = 7}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 76 $ $ x = \dfrac{76}{2} $ ${x = 38}$ Now that you know ${x = 38}$ , plug it back into $ {x+y = 69}$ to find $y$ ${(38)}{ + y = 69}$ ${y = 31}$ You can also plug ${x = 38}$ into $ {x-y = 7}$ and get the same answer for $y$ ${(38)}{ - y = 7}$ ${y = 31}$ Therefore, the larger number is $38$, and the smaller number is $31$.